Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.

中文翻译：

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处理网络实时估计中的计算-通信权衡和传感器选择

电子学的最新进展使得能够在网络系统的每个节点（机器人、传感器）上执行大量处理。本地处理支持数据压缩并可以减轻测量噪声，但与中央计算机相比，它仍然较慢（它需要更大的计算延迟）。然而，虽然节点可以并行处理数据，但集中计算本质上是顺序的。另一方面，如果节点将原始数据发送到中央计算机进行处理，则会导致通信延迟。这导致了基本的通信-计算权衡，其中每个节点必须决定最佳的预处理量以最大化网络性能。我们考虑一个负责估计动态系统状态的网络并提供三个贡献。第一的，我们为存在延迟的处理网络中的最佳实时估计提供了严格的问题公式。其次，我们表明，在监控连续时间标量线性系统的同构网络（其中所有传感器具有相同计算）的情况下，可以分析计算最大化网络估计性能的局部预处理的最佳量。第三，我们考虑异构网络监控离散时间多变量线性系统的现实情况，并提供算法来决定每个节点的合适预处理，并在计算约束使得使用所有传感器都不是最优的时选择传感器子集。数值模拟表明，选择传感器至关重要。此外，我们表明，如果节点应用我们算法建议的预处理策略，